I mean, to be fair he has so far stayed (mostly) democratic, with the KPD banning being the pnly arguable infringement (which tbf as well was not underserved, and I would only recriminate not banning the far right as well).
Given that his popularity is likely to only grow from here, I don't see why he would need to go out of his way to erode democratic institutions. It won't be perfect democracy, but I would say he'll probably maintain a decent standard.
As for the Cold War, it would be more alike to the pre-WW1 era than the OTL Cold War. There was a fundamental ideological gap that made the Cold War what it was, that could never happen between capitalist western european powers. You might have the disputes for influence and war scares, but you'd never have anything resembling the Iron Curtain.
I'd rather not, tbh. Too cliché, and given that the Kaiser would replace the office of President, Lettow-Vorbeck has reasons to avoid it. Also, Wilhelm III was an imbecile.